Pattern Formation in the Brusselator Model Using Numerical Bifurcation Analysis

Abstract

Pattern formation is one of the most surprising natural phenomena in real life. Analysis of spatiotemporal reaction-diffusion system can lead to understanding the pattern dynamics. However, the periodic traveling wave solutions resulting from the reaction-diffusion system can play an important role to explain the pattern dynamics. In this study, we analyze a system of nonlinear reaction-diffusion equations called the Brusselator model. We establish a parameter plane to investigate the existence of periodic traveling waves as well as stability results of the model using the method of continuation. We also find an Eckhaus type stability boundary where we confirm the stability change by calculating the essential spectra of the solutions of the model. As a result, we obtain a pattern transition from stripe pattern to spot pattern of the model in the two spatial dimensions numerically